On the $(m,r,s)$-halves of a Riordan array and applications
Received:May 10, 2022  Revised:July 10, 2022
Key Words: Riordan array   central coefficients   Pascal matrix   Delannoy matrix   Fibonacci numbers   Pell numbers   Jacobsthal numbers.  
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Lin Yang Lanzhou University of Technology No.287 Langongping Road Qilihe District,Lanzhou City,Gansu,P.R.China
Sheng-Liang Yang Lanzhou University of Technology No.287 Langongping Road Qilihe District,Lanzhou City,Gansu,P.R.China
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Abstract:
      Given a Riordan array, its vertical half and horizontal half are studied separately before. In the present paper, we introduce the $(m,r,s)$-halves of a Riordan array. This allows us to discuss the vertical half and horizontal half in a uniform context. As applications, we find several new identities involving Fibonacci, Pell, and Jacobsthal sequences by applying the $(m,r,s)$-halves of Pascal and Delannoy matrices.
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